Regular induced subgraphs of a random Graph

Michael Krivelevich; Benny Sudakov; Nicholas Wormald

doi:10.1002/rsa.20324

Regular induced subgraphs of a random Graph

Michael Krivelevich, Benny Sudakov, Nicholas Wormald

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

An old problem of Erdos, Fajtlowicz, and Staton asks for the order of a largest induced regular subgraph that can be found in every graph on $n$ vertices. Motivated by this problem, we consider the order of such a subgraph in a typical graph on $n$ vertices, i.e., in a binomial random graph $G(n,1/2)$. We prove that with high probability a largest induced regular subgraph of $G(n,1/2)$ has about $n^{2/3}$ vertices.

Original language	English
Pages (from-to)	235-250
Number of pages	16
Journal	Random Structures and Algorithms
Volume	38
Issue number	3
DOIs	https://doi.org/10.1002/rsa.20324
State	Published - May 2011

Keywords

Extremal graph theory
Random graph
Random regular graphs
Regular induced subgraph

All Science Journal Classification (ASJC) codes

Software
Applied Mathematics
General Mathematics
Computer Graphics and Computer-Aided Design

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10.1002/rsa.20324

Cite this

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JF - Random Structures and Algorithms

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ER -

Regular induced subgraphs of a random Graph

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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